Factor Calculator

Factors of 721

The factors of 721 are 1, 7, 103, and 721. In total, 721 has 4 factors. Its prime factorization is 7 × 103, and the sum of all its factors is 832.

All factors of 721

Here are all 4 factors of 721, listed from smallest to largest.

17103721

Factor pairs of 721

These 2 pairs of whole numbers each multiply to give 721.

1 × 721 = 721
7 × 103 = 721

Prime factorization of 721

Dividing 721 by the smallest prime at each step gives its prime factorization:

721 ÷ 7 = 103
103 ÷ 103 = 1
Result: 721 = 7 × 103 = 7 × 103

The distinct prime factors of 721 are 7, 103. To factorize any other number, use the prime factorization calculator.

Factor tree of 721

A factor tree shows the same prime factorization visually. Each composite branch splits until every endpoint is a prime number.

Factor tree of 7217217103
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 721

Number of factors4
Sum of factors832
Sum of proper factors111
Prime factorization7 × 103
Prime or composite?Composite
Even or odd?Odd
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 721 interesting

  • 721 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 2 different ways.
  • 721 is a deficient number: its proper factors sum to 111, which is 610 less than 721 itself.

How to find the factors of 721 yourself

Divide 721 by each whole number starting from 1. Whenever the division leaves no remainder, both the divisor and the quotient are factors. You only need to test up to √72126.85, because every factor above that pairs with one below it.

721 ÷ 1 = 721
721 ÷ 7 = 103

Reading both columns gives every factor: 1, 7, 103, 721. The factor calculator does this automatically for any number.

Frequently asked questions about 721

What are the factors of 721?

The factors of 721 are 1, 7, 103, and 721. That is 4 factors in total, counting both 1 and 721.

Is 721 a prime number?

No, 721 is not prime — it is a composite number with 4 factors. A prime number has exactly two factors, but 721 is also divisible by 7.

What is the prime factorization of 721?

The prime factorization of 721 is 7 × 103. Written out in full: 7 × 103 = 721. Its distinct prime factors are 7, 103.

What two numbers multiply to give 721?

There are 2 pairs of whole numbers that multiply to 721: 1 × 721, 7 × 103.

What is the sum of the factors of 721?

Adding all the factors of 721 together gives 832. Excluding 721 itself, the proper factors sum to 111.

Is 721 a perfect square?

No, 721 is not a perfect square. There is no whole number that multiplies by itself to give 721. The nearest perfect squares are 676 and 729.

What is the largest factor of 721 other than itself?

The largest factor of 721 apart from 721 itself is 103, since 721 ÷ 103 = 7.

How many factors does 721 have?

721 has 4 factors: 1, 7, 103, and 721. You can verify this from the prime factorization 7 × 103: add 1 to each exponent and multiply, giving 2 × 2 = 4.

Explore more

Try another number in the factor calculator, break 721 down further with the prime factorization calculator, or compare 721 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.